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            <small>
              <a href="#Procedure">Procedure<br></a>
              <a href="#Abstract">Abstract<br></a>
              <a href="#Required_Reading">Required_Reading<br></a>
              <a href="#Keywords">Keywords<br></a>
              <a href="#Brief_I/O">Brief_I/O<br></a>
              <a href="#Detailed_Input">Detailed_Input<br></a>

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              <small>               <a href="#Detailed_Output">Detailed_Output<br></a>
              <a href="#Parameters">Parameters<br></a>
              <a href="#Exceptions">Exceptions<br></a>
              <a href="#Files">Files<br></a>
              <a href="#Particulars">Particulars<br></a>
              <a href="#Examples">Examples<br></a>

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              </td>
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              <small>               <a href="#Restrictions">Restrictions<br></a>
              <a href="#Literature_References">Literature_References<br></a>
              <a href="#Author_and_Institution">Author_and_Institution<br></a>
              <a href="#Version">Version<br></a>
              <a href="#Index_Entries">Index_Entries<br></a>
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<h4><a name="Procedure">Procedure</a></h4>
<PRE>
   void spkapp_c ( SpiceInt             targ,
                   SpiceDouble          et,
                   ConstSpiceChar     * ref,
                   ConstSpiceDouble     sobs   [6],
                   ConstSpiceChar     * abcorr,
                   SpiceDouble          starg  [6],
                   SpiceDouble        * lt         ) 

</PRE>
<h4><a name="Abstract">Abstract</a></h4>
<PRE>
 
   Deprecated: This routine has been superseded by <a href="spkaps_c.html">spkaps_c</a>. This
   routine is supported for purposes of backward compatibility only.

   Return the state (position and velocity) of a target body 
   relative to an observer, optionally corrected for light time and 
   stellar aberration. 
 </PRE>
<h4><a name="Required_Reading">Required_Reading</a></h4>
<PRE>
 
   <a href="../req/spk.html">SPK</a> 
 </PRE>
<h4><a name="Keywords">Keywords</a></h4>
<PRE>
 
   EPHEMERIS 
 

</PRE>
<h4><a name="Brief_I/O">Brief_I/O</a></h4>
<PRE>
 
   Variable  I/O  Description 
   --------  ---  -------------------------------------------------- 
   targ       I   Target body. 
   et         I   Observer epoch. 
   ref        I   Inertial reference frame of observer's state. 
   sobs       I   State of observer wrt. solar system barycenter. 
   abcorr     I   Aberration correction flag. 
   starg      O   State of target. 
   lt         O   One way light time between observer and target. 
 </PRE>
<h4><a name="Detailed_Input">Detailed_Input</a></h4>
<PRE>
 
   targ        is the NAIF ID code for a target body.  The target 
               and observer define a state vector whose position 
               component points from the observer to the target. 
 
   et          is the ephemeris time, expressed as seconds past J2000 
               TDB, at which the state of the target body relative to 
               the observer is to be computed. 'et' refers to time at 
               the observer's location. 
 
   ref         is the inertial reference frame with respect to which 
               the observer's state 'sobs' is expressed. 'ref' must be 
               recognized by the SPICE Toolkit.  The acceptable 
               frames are listed in the Frames Required Reading, as 
               well as in the CSPICE routine chgirf_. 
 
               Case and blanks are not significant in the string 'ref'. 
 
   sobs        is the geometric (uncorrected) state of the observer 
               relative to the solar system barycenter at epoch 'et'. 
               'sobs' is a 6-vector:  the first three components of 
               'sobs' represent a Cartesian position vector; the last 
               three components represent the corresponding velocity 
               vector. 'sobs' is expressed relative to the inertial 
               reference frame designated by 'ref'. 
 
               Units are always km and km/sec. 
 
   abcorr      indicates the aberration corrections to be applied 
               to the state of the target body to account for one-way 
               light time and stellar aberration.  See the discussion 
               in the Particulars section for recommendations on  
               how to choose aberration corrections. 
                 
               abcorr may be any of the following: 
 
                  &quot;NONE&quot;     Apply no correction. Return the  
                             geometric state of the target body  
                             relative to the observer.   
 
               The following values of abcorr apply to the 
               &quot;reception&quot; case in which photons depart from the 
               target's location at the light-time corrected epoch 
               et-lt and *arrive* at the observer's location at 'et': 
 
                  &quot;LT&quot;       Correct for one-way light time (also 
                             called &quot;planetary aberration&quot;) using a 
                             Newtonian formulation. This correction 
                             yields the state of the target at the 
                             moment it emitted photons arriving at 
                             the observer at 'et'. 
  
                             The light time correction involves 
                             iterative solution of the light time 
                             equation (see Particulars for details). 
                             The solution invoked by the &quot;LT&quot; option 
                             uses one iteration. 
 
                  &quot;LT+S&quot;     Correct for one-way light time and 
                             stellar aberration using a Newtonian 
                             formulation. This option modifies the 
                             state obtained with the &quot;LT&quot; option to 
                             account for the observer's velocity 
                             relative to the solar system 
                             barycenter. The result is the apparent 
                             state of the target---the position and 
                             velocity of the target as seen by the 
                             observer. 
 
                  &quot;CN&quot;       Converged Newtonian light time 
                             correction.  In solving the light time 
                             equation, the &quot;CN&quot; correction iterates 
                             until the solution converges (three 
                             iterations on all supported platforms). 
 
                             The &quot;CN&quot; correction typically does not 
                             substantially improve accuracy because 
                             the errors made by ignoring 
                             relativistic effects may be larger than 
                             the improvement afforded by obtaining 
                             convergence of the light time solution. 
                             The &quot;CN&quot; correction computation also  
                             requires a significantly greater number 
                             of CPU cycles than does the  
                             one-iteration light time correction. 
 
                  &quot;CN+S&quot;     Converged Newtonian light time 
                             and stellar aberration corrections. 
 
 
               The following values of abcorr apply to the 
               &quot;transmission&quot; case in which photons *depart* from 
               the observer's location at 'et' and arrive at the 
               target's location at the light-time corrected epoch 
               et+lt: 
 
                  &quot;XLT&quot;      &quot;Transmission&quot; case:  correct for 
                             one-way light time using a Newtonian 
                             formulation. This correction yields the 
                             state of the target at the moment it 
                             receives photons emitted from the 
                             observer's location at 'et'. 
 
                  &quot;XLT+S&quot;    &quot;Transmission&quot; case:  correct for 
                             one-way light time and stellar 
                             aberration using a Newtonian 
                             formulation  This option modifies the 
                             state obtained with the &quot;XLT&quot; option to 
                             account for the observer's velocity 
                             relative to the solar system 
                             barycenter. The position component of 
                             the computed target state indicates the 
                             direction that photons emitted from the 
                             observer's location must be &quot;aimed&quot; to 
                             hit the target. 
 
                  &quot;XCN&quot;      &quot;Transmission&quot; case:  converged  
                             Newtonian light time correction. 
 
                  &quot;XCN+S&quot;    &quot;Transmission&quot; case:  converged  
                             Newtonian light time and stellar  
                             aberration corrections. 
 
               Neither special nor general relativistic effects are 
               accounted for in the aberration corrections applied 
               by this routine. 
 
               Case and blanks are not significant in the string 
               abcorr. 
 </PRE>
<h4><a name="Detailed_Output">Detailed_Output</a></h4>
<PRE>
 
   starg       is a Cartesian state vector representing the position 
               and velocity of the target body relative to the 
               specified observer. 'starg' is corrected for the 
               specified aberrations, and is expressed with respect 
               to the specified inertial reference frame.  The first 
               three components of 'starg' represent the x-, y- and 
               z-components of the target's position; last three 
               components form the corresponding velocity vector.

               Units are always km and km/sec.
 
               The position component of 'starg' points from the 
               observer's location at 'et' to the aberration-corrected 
               location of the target. Note that the sense of the 
               position vector is independent of the direction of 
               radiation travel implied by the aberration 
               correction. 
 
               The velocity component of 'starg' is obtained by 
               evaluating the target's geometric state at the light 
               time corrected epoch, so for aberration-corrected 
               states, the velocity is not precisely equal to the 
               time derivative of the position. 
  
   lt          is the one-way light time between the observer and 
               target in seconds.  If the target state is corrected
               for aberrations, then 'lt' is the one-way light time
               between the observer and the light time corrected
               target location. 
 </PRE>
<h4><a name="Parameters">Parameters</a></h4>
<PRE>
 
   None. 
 </PRE>
<h4><a name="Exceptions">Exceptions</a></h4>
<PRE>
 
   1) If the value of abcorr is not recognized, the error 
      SPICE(SPKINVALIDOPTION) is signaled. 
 
   2) If the reference frame requested is not a recognized 
      inertial reference frame, the error SPICE(BADFRAME)  
      is signaled. 
 
   3) If the state of the target relative to the solar system 
      barycenter cannot be computed, the error will be diagnosed  
      by routines in the call tree of this routine. 
 </PRE>
<h4><a name="Files">Files</a></h4>
<PRE>
 
   This routine computes states using SPK files that have been 
   loaded into the SPICE system, normally via the kernel loading 
   interface routine <a href="furnsh_c.html">furnsh_c</a>.  Application programs typically load 
   kernels once before this routine is called, for example during 
   program initialization; kernels need not be loaded repeatedly. 
   See the routine <a href="furnsh_c.html">furnsh_c</a> and the SPK and KERNEL Required Reading 
   for further information on loading (and unloading) kernels. 
 
   If any of the ephemeris data used to compute 'starg' are expressed 
   relative to a non-inertial frame in the SPK files providing those 
   data, additional kernels may be needed to enable the reference 
   frame transformations required to compute the state.  Normally 
   these additional kernels are PCK files or frame kernels.  Any 
   such kernels must already be loaded at the time this routine is 
   called. 
 </PRE>
<h4><a name="Particulars">Particulars</a></h4>
<PRE>
 
   In space science or engineering applications one frequently 
   wishes to know where to point a remote sensing instrument, such 
   as an optical camera or radio antenna, in order to observe or 
   otherwise receive radiation from a target.  This pointing problem 
   is complicated by the finite speed of light:  one needs to point 
   to where the target appears to be as opposed to where it actually 
   is at the epoch of observation.  We use the adjectives 
   &quot;geometric,&quot; &quot;uncorrected,&quot; or &quot;true&quot; to refer to an actual 
   position or state of a target at a specified epoch.  When a 
   geometric position or state vector is modified to reflect how it 
   appears to an observer, we describe that vector by any of the 
   terms &quot;apparent,&quot; &quot;corrected,&quot; &quot;aberration corrected,&quot; or &quot;light 
   time and stellar aberration corrected.&quot; 
 
   The SPICE Toolkit can correct for two phenomena affecting the 
   apparent location of an object:  one-way light time (also called 
   &quot;planetary aberration&quot;) and stellar aberration.  Correcting for 
   one-way light time is done by computing, given an observer and 
   observation epoch, where a target was when the observed photons 
   departed the target's location.  The vector from the observer to 
   this computed target location is called a &quot;light time corrected&quot; 
   vector.  The light time correction depends on the motion of the 
   target, but it is independent of the velocity of the observer 
   relative to the solar system barycenter. Relativistic effects 
   such as light bending and gravitational delay are not accounted 
   for in the light time correction performed by this routine. 
 
   The velocity of the observer also affects the apparent location 
   of a target:  photons arriving at the observer are subject to a 
   &quot;raindrop effect&quot; whereby their velocity relative to the observer 
   is, using a Newtonian approximation, the photons' velocity 
   relative to the solar system barycenter minus the velocity of the 
   observer relative to the solar system barycenter.  This effect is 
   called &quot;stellar aberration.&quot;  Stellar aberration is independent 
   of the velocity of the target.  The stellar aberration formula 
   used by this routine is non-relativistic. 
 
   Stellar aberration corrections are applied after light time 
   corrections:  the light time corrected target position vector is  
   used as an input to the stellar aberration correction. 
 
   When light time and stellar aberration corrections are both 
   applied to a geometric position vector, the resulting position  
   vector indicates where the target &quot;appears to be&quot; from the 
   observer's location.   
 
   As opposed to computing the apparent position of a target, one 
   may wish to compute the pointing direction required for  
   transmission of photons to the target.  This requires correction 
   of the geometric target position for the effects of light time and 
   stellar aberration, but in this case the corrections are computed 
   for radiation traveling from the observer to the target.  
 
   The &quot;transmission&quot; light time correction yields the target's 
   location as it will be when photons emitted from the observer's 
   location at 'et' arrive at the target.  The transmission stellar 
   aberration correction is the inverse of the traditional stellar 
   aberration correction:  it indicates the direction in which 
   radiation should be emitted so that, using a Newtonian 
   approximation, the sum of the velocity of the radiation relative 
   to the observer and of the observer's velocity, relative to the  
   solar system barycenter, yields a velocity vector that points in  
   the direction of the light time corrected position of the target. 
  
   The traditional aberration corrections applicable to observation  
   and those applicable to transmission are related in a simple way: 
   one may picture the geometry of the &quot;transmission&quot; case by  
   imagining the &quot;observation&quot; case running in reverse time order, 
   and vice versa.   
 
   One may reasonably object to using the term &quot;observer&quot; in the 
   transmission case, in which radiation is emitted from the 
   observer's location.  The terminology was retained for 
   consistency with earlier documentation. 
 
   Below, we indicate the aberration corrections to use for some 
   common applications: 
 
      1) Find the apparent direction of a target for a remote-sensing 
         observation: 
 
            Use &quot;LT+S&quot;:  apply both light time and stellar  
            aberration corrections. 
 
         Note that using light time corrections alone (&quot;LT&quot;) is 
         generally not a good way to obtain an aproximation to an 
         apparent target vector:  since light time and stellar 
         aberration corrections often partially cancel each other, 
         it may be more accurate to use no correction at all than to 
         use light time alone. 
 
 
      2) Find the corrected pointing direction to radiate a signal 
         to a target:   
 
            Use &quot;XLT+S&quot;:  apply both light time and stellar  
            aberration corrections for transmission. 
 
 
      3) Obtain an uncorrected state vector derived directly from  
         data in an SPK file: 
 
            Use &quot;NONE&quot;. 
 
 
      4) Compute the apparent position of a target body relative 
         to a star or other distant object: 
 
            Use &quot;LT&quot; or &quot;LT+S&quot; as needed to match the correction 
            applied to the position of the distant object.  For 
            example, if a star position is obtained from a catalog, 
            the position vector may not be corrected for stellar 
            aberration.  In this case, to find the angular 
            separation of the star and the limb of a planet, the 
            vector from the observer to the planet should be 
            corrected for light time but not stellar aberration. 
 
 
      5) Use a geometric state vector as a low-accuracy estimate 
         of the apparent state for an application where execution  
         speed is critical: 
 
            Use &quot;NONE&quot;. 
 
 
      6) While this routine cannot perform the relativistic 
         aberration corrections required to compute states 
         with the highest possible accuracy, it can supply the 
         geometric states required as inputs to these computations: 
 
            Use &quot;NONE&quot;, then apply high-accuracy aberration 
            corrections (not available in the SPICE Toolkit). 
 
 
   Below, we discuss in more detail how the aberration corrections 
   applied by this routine are computed.      
 
 
   Geometric case 
   ============== 
 
      <b>spkapp_c</b> begins by computing the geometric position T(et) of the 
      target body relative to the solar system barycenter (SSB). 
      Subtracting the geometric position of the observer O(et) gives 
      the geometric position of the target body relative to the 
      observer. The one-way light time, 'lt', is given by 
 
                | T(et) - O(et) | 
         lt = ------------------- 
                        c 
 
      The geometric relationship between the observer, target, and 
      solar system barycenter is as shown: 
 
 
         SSB ---&gt; O(et) 
          |      / 
          |     / 
          |    /                            
          |   /  T(et) - O(et)   
          V  V                                   
         T(et) 
 
 
      The returned state consists of the position vector 
 
         T(et) - O(et) 
 
      and a velocity obtained by taking the difference of the 
      corresponding velocities.  In the geometric case, the  
      returned velocity is actually the time derivative of the  
      position. 
 
 
   Reception case 
   ============== 
 
      When any of the options &quot;LT&quot;, &quot;CN&quot;, &quot;LT+S&quot;, &quot;CN+S&quot; is 
      selected, <b>spkapp_c</b> computes the position of the target body at 
      epoch et-lt, where 'lt' is the one-way light time.  Let T(t) and 
      O(t) represent the positions of the target and observer 
      relative to the solar system barycenter at time t; then 'lt' is 
      the solution of the light-time equation 
 
                | T(et-lt) - O(et) | 
         lt = ------------------------                            (1) 
                         c 
 
      The ratio  
 
          | T(et) - O(et) | 
        ---------------------                                     (2) 
                  c 
 
      is used as a first approximation to 'lt'; inserting (2) into the 
      RHS of the light-time equation (1) yields the &quot;one-iteration&quot; 
      estimate of the one-way light time. Repeating the process 
      until the estimates of 'lt' converge yields the &quot;converged 
      Newtonian&quot; light time estimate. 
      
      Subtracting the geometric position of the observer O(et) gives 
      the position of the target body relative to the observer: 
      T(et-lt) - O(et). 
 
         SSB ---&gt; O(et) 
          | \     | 
          |  \    | 
          |   \   | T(et-lt) - O(et) 
          |    \  | 
          V     V V 
         T(et)  T(et-lt) 
       
      The position component of the light-time corrected state  
      is the vector 
 
         T(et-lt) - O(et) 
 
      The velocity component of the light-time corrected state  
      is the difference 
 
         T_vel(et-lt) - O_vel(et) 
           
      where T_vel and O_vel are, respectively, the velocities of 
      the target and observer relative to the solar system  
      barycenter at the epochs et-lt and 'et'. 
 
      If correction for stellar aberration is requested, the target 
      position is rotated toward the solar system barycenter- 
      relative velocity vector of the observer. The rotation is 
      computed as follows: 
 
         Let r be the light time corrected vector from the observer 
         to the object, and v be the velocity of the observer with 
         respect to the solar system barycenter. Let w be the angle 
         between them. The aberration angle phi is given by 
 
            sin(phi) = v sin(w) / c 
 
         Let h be the vector given by the cross product 
 
            h = r X v 
 
         Rotate r by phi radians about h to obtain the apparent 
         position of the object. 
 
      The velocity component of the output state 'starg' is  
      not corrected for stellar aberration. 
 
 
   Transmission case 
   ================== 
 
      When any of the options &quot;XLT&quot;, &quot;XCN&quot;, &quot;XLT+S&quot;, &quot;XCN+S&quot; are 
      selected, <b>spkapp_c</b> computes the position of the target body T at 
      epoch et+lt, where 'lt' is the one-way light time. 'lt' is the 
      solution of the light-time equation 
 
                | T(et+lt) - O(et) | 
         lt = ------------------------                            (3) 
                          c 
 
      Subtracting the geometric position of the observer, O(et), 
      gives the position of the target body relative to the 
      observer: T(et-lt) - O(et). 
 
                 SSB --&gt; O(et) 
                / |    *  
               /  |  *  T(et+lt) - O(et)   
              /   |*      
             /   *|     
            V  V  V      
        T(et+lt)  T(et)     
 
      The position component of the light-time corrected state  
      is the vector 
 
         T(et+lt) - O(et) 
 
      The velocity component of the light-time corrected state  
      is the difference 
 
         T_vel(et+lt) - O_vel(et) 
           
      where T_vel and O_vel are, respectively, the velocities of 
      the target and observer relative to the solar system  
      barycenter at the epochs et+lt and 'et'. 
 
      If correction for stellar aberration is requested, the target 
      position is rotated away from the solar system barycenter- 
      relative velocity vector of the observer. The rotation is 
      computed as in the reception case, but the sign of the 
      rotation angle is negated. 
 
      The velocity component of the output state 'starg' is  
      not corrected for stellar aberration. 
 
   Neither special nor general relativistic effects are accounted  
   for in the aberration corrections performed by this routine. 
 </PRE>
<h4><a name="Examples">Examples</a></h4>
<PRE>
 
   In the following code fragment, <a href="spkssb_c.html">spkssb_c</a> and <b>spkapp_c</b> are used 
   to display the position of Io (body 501) as seen from the  
   Voyager 2 spacecraft (Body -32) at a series of epochs. 
 
   Normally, one would call the high-level reader <a href="spkezr_c.html">spkezr_c</a> to obtain 
   state vectors.  The example below illustrates the interface 
   of this routine but is not intended as a recommendation on 
   how to use the CSPICE SPK subsystem. 
 
   The use of integer ID codes is necessitated by the low-level 
   interface of this routine. 

 
      #include &lt;stdio.h&gt;
      #include &quot;SpiceUsr.h&quot;
      
      #define  IO       501
      #define  VG2      -32
                 .
                 .
                 .
          [ load kernels ]
                 .
                 .
                 .
      while ( epoch &lt;= end )
      {
         <a href="spkssb_c.html">spkssb_c</a> ( VG2, epoch, &quot;J2000&quot;, stvg2                  );
         <b>spkapp_c</b> ( IO,  epoch, &quot;J2000&quot;, stvg2, &quot;LT&quot;, stio, &amp;lt ); 

         <a href="recrad_c.html">recrad_c</a> ( stio, &amp;range, &amp;ra, &amp;dec ); 
         
         printf ( &quot;RA = %f,  DEC = %f\n&quot;,  ra*<a href="dpr_c.html">dpr_c</a>(), dec*<a href="dpr_c.html">dpr_c</a>() );
 
         epoch += delta; 
      }
</PRE>
<h4><a name="Restrictions">Restrictions</a></h4>
<PRE>
 
   1) The kernel files to be used by <b>spkapp_c</b> must be loaded 
      (normally by the CSPICE kernel loader <a href="furnsh_c.html">furnsh_c</a>) before  
      this routine is called. 
 
   2) Unlike most other SPK state computation routines, this 
      routine requires that the input state be relative to an 
      inertial reference frame.  Non-inertial frames are not 
      supported by this routine. 
 
   3) In a future version of this routine, the implementation  
      of the aberration corrections may be enhanced to improve 
      accuracy.      
 </PRE>
<h4><a name="Literature_References">Literature_References</a></h4>
<PRE>
 
   SPK Required Reading. 
 </PRE>
<h4><a name="Author_and_Institution">Author_and_Institution</a></h4>
<PRE>
 
   N.J. Bachman    (JPL) 
   H.A. Neilan     (JPL) 
   I.M. Underwood  (JPL) 
   W.L. Taber      (JPL) 
 </PRE>
<h4><a name="Version">Version</a></h4>
<PRE>
   -CSPICE Version 2.0.3, 19-MAY-2010 (BVS)

       Index lines now state that this routine is deprecated.

   -CSPICE Version 2.0.2, 08-JAN-2008 (NJB)

       The Abstract section of the header was updated to
       indicate that this routine has been deprecated.
 
   -CSPICE Version 2.0.1, 13-OCT-2003 (EDW)

       Various minor header changes were made to improve clarity.
       Added mention that 'lt' returns a value in seconds.

   -CSPICE Version 2.0.0, 19-DEC-2001 (NJB)

       Updated to handle aberration corrections for transmission
       of radiation.  Formerly, only the reception case was
       supported.  The header was revised and expanded to explain
       the functionality of this routine in more detail.

   -CSPICE Version 1.0.0, 21-JUN-1999 (NJB) (HAN) (IMU) (WLT)
</PRE>
<h4><a name="Index_Entries">Index_Entries</a></h4>
<PRE>
 
   DEPRECATED low-level aberration correction 
   DEPRECATED apparent state from spk file 
   DEPRECATED get apparent state 
 </PRE>
<h4>Link to routine spkapp_c source file <a href='../../../src/cspice/spkapp_c.c'>spkapp_c.c</a> </h4>

      </td>
    </tr>
  </tbody>
</table>

   <pre>Wed Jun  9 13:05:30 2010</pre>

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